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What Would Happen If An Airplane Door Burst Open Mid-Flight?

Has this terrible thought ever crossed your mind while you were sitting on a plane trying to relax? The chance of this happening is pretty slim. But, if you have seen movies like Final Destination or Non-Stop, you get the idea of what would happen.

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The calculation of the “real world” pressure in a constriction of a tube is difficult to do because of viscous losses, turbulence, and the assumptions which must be made about the velocity profile (which affect the calculated kinetic energy). The model calculation here assumes laminar flow (no turbulence), assumes that the distance from the larger diameter to the smaller is short enough that viscous losses can be neglected, and assumes that the velocity profile follows that of theoretical laminar flow. Specifically, this involves assuming that the effective flow velocity is one half of the maximum velocity, and that the average kinetic energy density is given by one third of the maximum kinetic energy density.

Now if you can swallow all those assumptions, you can model* the flow in a tube where the volume flowrate is = cm3/s and the fluid density is ρ = gm/cm3. For an inlet tube area A1= cm2 (radius r1 =cm), the geometry of flow leads to an effective fluid velocity of v1 =cm/s. Since the Bernoulli equation includes the fluid potential energy as well, the height of the inlet tube is specified as h1 = cm. If the area of the tube is constricted to A2=cm2 (radius r2 = cm), then without any further assumptions the effective fluid velocity in the constriction must be v2 = cm/s. The height of the constricted tube is specified as h2 = cm.

The kinetic energy densities at the two locations in the tube can now be calculated, and the Bernoulli equation applied to constrain the process to conserve energy, thus giving a value for the pressure in the constriction. First, specify a pressure in the inlet tube:
Inlet pressure = P1 = kPa = lb/in2 = mmHg = atmos.
The energy densities can now be calculated. The energy unit for the CGS units used is the erg.
Inlet tube energy densities
Kinetic energy density = erg/cm3
Potential energy density = erg/cm3
Pressure energy density = erg/cm3
Constricted tube energy densities
Kinetic energy density = erg/cm3
Potential energy density = erg/cm3
Pressure energy density = erg/cm3
The pressure energy density in the constricted tube can now be finally converted into more conventional pressure units to see the effect of the constricted flow on the fluid pressure:

This calculation can give some perspective on the energy involved in fluid flow, but it’s accuracy is always suspect because of the assumption of laminar flow. For typical inlet conditions, the energy density associated with the pressure will be dominant on the input side; after all, we live at the bottom of an atmospheric sea which contributes a large amount of pressure energy. If a drastic enough reduction in radius is used to yield a pressure in the constriction which is less than atmospheric pressure, there is almost certainly some turbulence involved in the flow into that constriction. Nevertheless, the calculation can show why we can get a significant amount of suction (pressure less than atmospheric) with an “aspirator” on a high pressure faucet. These devices consist of a metal tube of reducing radius with a side tube into the region of constricted radius for suction.

*Note: Some default values will be entered for some of the values as you start exploring the calculation. All of them can be changed as a part of your calculation.

Reblogged this on SERENDIPITY and commented:
Been seeing too many scary thrillers where they pop open airplane door and you get sucked out into … nothing? Apparently someone else was worried too. Here you go!